Adding and Subtracting Functions
Procedure â€”
To Evaluate the Sum or Difference of Functions
Step 1 Use x = a to find f(a) and g(a)
Step 2 Find f(a) + g(a) or f(a)  g(a).
Example 1
Given f(x) = x^{3}  9 and g(x) = x^{2} + 18, find (f + g)(x) when x
= 2.
That is, find (f + g)(2).
Solution
Step 1 
Use x = 2 to find f(2) and g(2). Substitute
2 for x in f(x).
Simplify.
Subtract.
So, f(2) = 17.
Substitute 2 for x in g(x).
Simplify.
Add.
So, g(2) = 22.

f(2)
g(2) 
= (2)^{3}  9 = 8  9
= 17 = (2)^{2} + 18 = 4 + 18 = 22 
Step 2 
Find f(2) = g(2).
Add. 
f(2) + g(2) 
= 17 + 22 = 5 
So, (f + g)(2) = 5.
Example 2
Given f(x) = x^{4} + 20 and g(x) = 5x^{2}, find (f  g)(x) when x
= 3.
That is, find (f  g)(3).
Solution
Step 1 
Use x = 3 to find f(3) and g(3). Substitute 3 for x in f(x).
Simplify.
So, f(3) = 101.
Substitute 3 for x in g(x).
Simplify.
So, g(3) = 45. 
f(3)
g(3) 
= (3)^{4} + 20
= 101 = 5(3)^{2} = 45 
Step 2 
Find f(3)  g(3).
Subtract. 
f(3)  g(3) 
= 101  45
= 56 
So, (f  g)(3) = 56.
